There is a huge academic literature on project manager competencies. However, the research has yet to confirm the project manager competencies that correlate with project success.
The Connected Papers schematic below provides a starting point for readers interested in exploring the literature further. The starting paper used is Senior management perceptions of project management competence | Connected Papers
Crawford, L., 2005. Senior management perceptions of project management competence. International journal of project management, 23(1), pp.7-16.
Müller, R. and Turner, R., 2010. Leadership competency profiles of successful project managers. International Journal of project management, 28(5), pp.437-448.
Partington, D., Pellegrinelli, S. and Young, M., 2005. Attributes and levels of programme management competence: an interpretive study. International Journal of Project Management, 23(2), pp.87-95.
Stevenson, D.H. and Starkweather, J.A., 2010. PM critical competency index: IT execs prefer soft skills. International journal of project management, 28(7), pp.663-671.